# CM2 FEM® SDK /full technical specifications

The right solution: modern, reliable, powerful and lighting fast, the CM2 FEM® Engines are written in standard C++ language.

They are easy to integrate into your applications.

They are easy to integrate into your applications.

### 1D Finite Elements /line meshes

- Beams: 2-node and 3-node, thin or thick theory (Euler-Bernouilli, Timoshenko).

Linear and non-linear (large strains & large displacements / rotations).

Relaxations, hard offsets, tapered beams (exact for 2-node linear beams). - Rod: 2-node linear.
- Cable: 2-node non-linear rod (large displacements, traction only).
- Distributed linear spring: 2-node and 3-node.
- Heat capacity lines: 2-node and 3-node.
- Heat conduction lines: 2-node and 3-node.
- Heat convection lines: 2-node and 3-node.

### 2D Finite Elements /plane and surface meshes

- Membrane triangles:

3- and 6-node (isoparametric). Linear and non-linear (large strains & large displacements). - Membrane quadrangles:

4- and 9-node (isoparametric). Linear and non-linear (large strains & large displacements). - Plane-strain triangles:

3- and 6-node (isoparametric). Linear and non-linear (large strains & large displacements). - Plane-strain quadrangles:

4- and 9-node (isoparametric). Linear and non-linear (large strains & large displacements). - 3-D axi-symmetric triangles:

3- and 6-node (isoparametric). Linear and non-linear (large strains & large displacements). - 3-D axi-symmetric quadrangles:

4- and 9-node (isoparametric). Linear and non-linear (large strains & large displacements). - Plate triangles (Mindlin):

3- and 6-node (isoparametric). Linear and non-linear (large strains & large displacements / rotations). - Plate quadrangles (Mindlin):

4- and 9-node (isoparametric). Linear and non-linear (large strains & large displacements / rotations). - Shell triangles (Mindlin):

3- and 6-node (isoparametric). Linear and non-linear (large strains & large displacements / rotations). - Shell quadrangles (Mindlin):

4- and 9-node (isoparametric). Linear and non-linear (large strains & large displacements / rotations). - Distributed plane spring triangles:

3- and 6-node (isoparametric). - Distributed plane spring quadrangles:

4- and 9-node (isoparametric). - Heat capacity surfaces: 3/6-node triangles, 4/9-node quadrangles (isoparametric).
- Heat conduction surfaces: 3/6-node triangles, 4/9-node quadrangles (isoparametric).
- Heat convection surfaces: 3/6-node triangles, 4/9-node quadrangles (isoparametric).

### 3D Finite Elements /solid meshes

(CM2 FEM® 3D only)

- Tetrahedrons:

4- and 10-node (isoparametric). Linear and non-linear (large strains & large displacements). - Pyramids:

5- and 14-node (isoparametric). Linear and non-linear (large strains & large displacements). - Wedges:

6- and 18-node (isoparametric). Linear and non-linear (large strains & large displacements). - Hexahedrons:

8- and 27-node (isoparametric). Linear and non-linear (large strains & large displacements). - Heat capacity solids: 4/10-node tetrahedrons, 5/15-node pyramids, 6/18-node wedges, 8/27-node hexahedrons (isoparametric).
- Heat conduction solids: 4/10-node tetrahedrons, 5/15-node pyramids, 6/18-node wedges, 8/27-node hexahedrons (isoparametric).

### Miscellaneous Finite Elements

- Springs (displacement or rotation).
- Links.
- Rigid bodies (small/large displacements/rotations).
- Rigid diaphragms (small/large displacements/rotations).
- Plane contacts.
- Cables.
- Hinges.
- Hard and soft offsets.
- User stiffness, user mass, user damping, user thermal matrix.
- Punctual masses (with offsets), diagonal masses, dash-pots, Rayleigh dampings.
- Punctual thermal capacity, punctual thermal convection.

### Analyses

- Static linear (mechanical, thermal).

Mixed loads (forces / displacements), thermal loads (with gradients), multiple load cases, combinations. - Matrix condensation (mechanical, thermal).

Stiffness, thermal conductivity. - Static non-linear (mechanical).

Newton-Raphson solver, large strains, large displacements, full non-linear buckling. - Euler buckling (mechanical).

Lanczos solver, windowing on critical loads. - Modal dynamic analysis (mechanical).

Lanczos solver, windowing on frequencies, “Load-dependent Ritz vectors” LDRV solver (mechanical). - Seismic analysis (mechanical).

Soil spectrum, participation factors, effective modal masses, CQC combination, correction due to the residual mode. - Transient dynamic analysis (mechanical, thermal).

Newmark implicit solver, time-dependent loads.

All solvers are multi-threaded (parallelized on multi-core CPUs) and support out-of-core management (managed swapping of global matrices).

Static linear and Matrix condensation (mechanical and thermal) are included in all flavours of CM2 FEM® 2D and CM2 FEM® 3D.

Static non-linear and Euler buckling are included in CM2 FEM® 2D Non-Linear and Full, CM2 FEM® 3D Non-Linear and Full.

Modal dynamic analysis, Seismic analysis and Transient dynamic analysis are included in CM2 FEM® 2D Dynamics and Full, CM2 FEM® 3D Dynamics and Full.

Static non-linear and Euler buckling are included in CM2 FEM® 2D Non-Linear and Full, CM2 FEM® 3D Non-Linear and Full.

Modal dynamic analysis, Seismic analysis and Transient dynamic analysis are included in CM2 FEM® 2D Dynamics and Full, CM2 FEM® 3D Dynamics and Full.

### Loads and boundary conditions

- Load-only models.
- Neumann boundary conditions: forces/momentums/heat flows.
- Dirichlet boundary conditions: prescribed displacements/rotations/temperatures.
- Mixed boundary conditions: Neumann + Dirichlet.
- Thermal loads: uniform, element-by-element, varying through element, varying through section/thickness.

All Loads and Boundary Conditions are included in all flavours of CM2 FEM® 2D and CM2 FEM® 3D.

### Constitutive Laws

- User-defined scalar laws: linear and non-linear.
- Distributed springs: 1D or 2D, linear or not.
- Hooke’s laws: 1D, 2D, plane-strains and 3D elements.
- Orthotropic laws: 2D (plane-strains, plates or shells) and 3D elements.
- Prandtl-Reuss elasto-plastic laws: 1D, plane-strains and 3D elements.

Von-Mises criterion + isotropic hardening: Ramberg-Osgood, power, perfect elasto-plastic.

All constitutive laws are included in all flavours of CM2 FEM® 2D and CM2 FEM® 3D.

### More specific needs?

Check our consulting and development services.